THREE ESSAYS ON CHANCE, CREDENCE AND PROBABILISTIC LAWS
- NICK BOSTROM
Lisa says that the probability that the coin will fall heads is 50%. She might just mean that she personally happens to believe, with a credence of 50%, that the coin will fall heads. In that case, she is making a statement about her subjective probability. However, she might well mean something stronger. She might mean that the situation is such that, objectively, there is a 50% probability of heads. The main question that these three essay will examine is what sort of thing such objective probabilities are.
The approach that will be taken here is in the tradition started by David Lewis (1980) and Brian Skyrms (1980). This tradition seeks to analyze objective probability in a way that would make objective probabilities supervene on the pattern of events in a world, a condition known as Humean Supervenience. Thus no problematic ontological commitments will be made, in contrast to approaches such as Mellor’s (1971, 1995), propensity interpretations (e.g. Popper 1959; Gillies 1973) or the hypothetical frequency interpretation (von Mises 1939). On the other hand, this tradition also differs from the actual frequency interpretation (e.g. [ref*** forthcoming Mind paper]): the chance-making patterns are not simply identified with actual frequencies of some type of events. Although typically objective probabilities will be similar to actual frequencies, especially if the relevant classes of events are large, there can be discrepancies.
The motivation for this "third-way" tradition (Hoefer 1999) is that it avoids the difficulties that have long been known to plague both propensity interpretations and actual frequency interpretations. I will not recap those difficulties here.
Essay I some shortcomings of Lewis’ theory of chance. This sets the stage for Essay II, where I will develop my own theory of chance (and the related notions of objective probability and propensity), a theory which overcomes the shortcomings of Lewis’ theory and brings some important other advantages as well. Essay III will examine the implications of my theory of chance for the analysis of laws. It is shown that the connection between chance and reasonable credence established in Essay II entail quite strong constrains on what can count as a successful explication of laws.
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